Old grid system – Atlas Florae Europaeae
The grid of Atlas Florae Europaeae volumes 1–12, with its 4419 grid cells, was modified from the Military Grid Reference System (MGRS). The MGRS itself is an alphanumeric version of a numerical UTM (Universal Transverse Mercator) or UPS (Universal Polar Stereographic) grid coordinate.
Fig. 1: AFE 1–12 used the 50 x 50 km quadrants of the MGRS 100 x 100 km squares as mapping units. The MGRS pattern was modified in AFE as follows:
 Numbers 1 to 4 to indicate the 50 km x 50 km quarters of the MGRS 100 km x 100 km squares. This coding, such as MG1, MG2, MG3 and MG4 (for the NW, SW, NE and SE quarters of the larger MGRS squares), is not supported by the MGRS.
Fig. 2: Black squares in the picture indicate grid cells which were not used. The records from them were moved to adjacent squares, or to grid cells in nonstandard position. Iceland, Svalbard and Azores not illustrated (there are plenty of similar cases in those areas, too).
 In coastal areas the squares with less than 10 % (250 km^{2}) of land, records were transferred into the nearest mainland square. However, islands far from the coast and long peninsulas had their own squares. Some of the deviations are listed below; an asterisk (*) indicates symbols of squares the circles of which deviate from the actual position of the UTM squares.
British Isles  The entire S. part of the Isle of Lewis is in PE2. All of North Uist (etc.) is in *ND3. All of S. South Uist (Barra, etc.) is in *ND4. Dunvegan Head is in PD3. All of the Isle of Man is in *UF4. All of the Scilly Isles are in PR4. UA2 is included in *UA1. UA4 is included in UA3. Guernsey and Sark are in WV1. Alderney and Jersey are in WV3. 
Denmark  All of Laesö is in *PJ1. All of Bornholm is in *VB4. Faeröerne are in *FaeN and *FaeS, the limit between them follows Skopen Fjord. 
Germany  Helgoland is in ME1. VA2 contains only E. RУМgen. 
Greece  The scheme from AFE vol. 3 (1976) – see Fig. 3 below. 
Iceland  All of Snaefellsnes is in *AN4. 
Italy  NP4 is included in PP2. *PN2 contains: all of Elba, Capraia, Pianosa, Montecristo, and islands W. of it. (Mainland on PN2 is included in PN4). UF2 also contains islands of UF4. All of Isole Eolie o Lipari are in *VC3. All of Pantelleria is in *QF3. All of Isole Pelagie are in *TV1. (All of Malta is in *VV1). 
Netherlands  All of Vlieland is in FU1. All of Terschelling is in FV4. 
Norway  Kjelmesöy and the peninsula E. of it are in VC2. *Björnöya and *Jan Mayen form a square of their own. Kvitöya is in *NK4. Kongsöya is in *NH1. Svensköya is in *MH4. Hopen is in *MF4. 
Portugal  Each island of the *Azores forms a square of its own. 
Russia  All of Poluostrov Rybachiy is in VC4. NW. Kanin is in *MB4. Ostrov Matveyev is in EB3, the rest of EC4 is included in EC3. All of Suursari is in NG1. Ostrov Malyy Tyutyarsari is in NG2. Kolka is in EJ3. Ostrov Dzharylgach is in VS4, Rybnoye in VR4. 
Spain  BD2 is included in *BC1. All of Isla of Ibiza is in *CD4. The entire W. part of Isla de Mallorca is in *DD3, the E. part in *ED1. All of Isla de Menorca is in *EE4. I. Alboran is in *VE3. 
Sweden  All of Gotska Sandön is in *CK3. All of Central Gotland is in *CJ1. W. edge of XD1 is in WD3, N. Öland is in XD2. 
Turkey (European part)  All of Imroz Ada is in ME2. PF4 is included in *PF3. 
Fig. 3: The scheme for Greece from AFE vol. 3 (1976).
Fig. 4: AFE grid pattern (not the actual grid; grid deviations omitted from this picture). Pale green = central seam square (two MGRS squares of different UTM zones merged, base width of the squares between 20–30 km); pale blue = seam square, widened for 10 km (base width 30–40 km); yellow = seam square with base width over 40 km; purple = narrow seam square (base width < 10 km merged with adjacent square in the same zone); red = seam square, narrowed 10 km; grey = rectanangular square, width 60 km; dark violet = rectangular square, base width 40 km; blue gridlines = MGRS grid in the UTM zone 34.
 The centre of grids covering isolated islands was put to the actual position of the island, irrespective of the standard grid. This resulted also in "polygonlike" grid cells, to include whole islands in a particular square.
 Certain individual mountain tops forming distinct biogeographic entities were not divided between two or more squares, despite of the grid.
 The square codes for all of Iceland deviated from the MGRS pattern.
To be able to limit the longitudinal width variation of the grid cells to 40 to 60 km, in the overlapping area between different UTM zones, the longitudinal limits of the grid cells were shifted outwards or inwards. When the standard MGRS squares extended into adjacent UTM zone, they were treated differently depending on the distance between the UTM zone boundary and the SW corner (if the square belongs to the zone west of the zone boundary) or SE corner (if in the eastern zone) of such seam squares. That distance, let's call it "x" below, is something between 0  slightly above 50 km (can be above 50 in some cases, for instance where a UTM zone boundary goes through the NE corner of a square at the zone border). The x values of 10, 20, 30, 40 kilometers influenced the treatment of the squares in AFE 1–12 this way:
Fig. 5: Eastern border of the UTM zone 34 in Estonia and Finland. Colours are explained as follows:

GREY = Parts of squares on the different sides of the zone boundary are merged if 40 <= x + x <= 60 km. This means for the squares to be merged, x must be between 20 and 30 km. Standard 10km UTM lines are followed here, and the merging has no effect on the width of the adjacent standard squares.

CYAN (DENSE BLUE DIAGONAL GRID SHOWS HOW THE WIDTH OF THE ADJACENT SQUARE IS CHANGED). If x is less than 20 km, the squares on different sides of the zone boundary are not merged, but the small parts of seam squares are joined the adjacent standard square. In cases where this would result in squares wider than 60 km, the width of the adjacent standard square is adjusted by narrowing its western or eastern edge (the edge farther from the zone border) to the next full 10km UTM easting. In these cases x + 50 <= 60 which means if x is between 10 and 20, this longitudinal shift affecting the width of adjacent standard squares is done. Thus the width of the next standard square also grows to 60 km.

YELLOW = If x is below 10 km, then slices are joined to the adjacent square without additionally reducing its width by 10 kilometers (and thus the next square remains as 50 km x 50 km square). Thus the width of the adjacent standard squares becomes something between 50 and 60 km.

PURPLE (PURPLE HORIZONTAL GRID SHOWS HOW THE WIDTH OF THE ADJACENT SQUARE IS CHANGED). If x is more than 30 km, but less than 40 km, the partial square are not joined to the adjacent standard square, they would become too wide. Instead the edge outwards of the zone is extended to the next full 10km UTM easting. Thus the grid cells become at least 40 km wide. Simultaneously the adjacent standard squares become 10 km narrower.

RED = If x is more than 40 km, the square is treated as an independent grid cell.
Fig. 6: AFE old grid pattern in N Europe (deviations from the general pattern not shown!).
References:
 Dana, Peter, H.: Coordinate Systems Overview.
 Defense Mapping Agency Technical Manual 8358.1 Datums, Ellipsoids, Grids and Grid Reference Systems.
Contents: Raino Lampinen, 2001