[Phoenix]

Thomas Poling married Elinor, some time pre 1684
Thomas Poling married Mary, sometime pre 1709
William Poling married Anne sometime pre 1747

The families were associated with Petersfield from the 1640s to gone 1800.
The name can be spelled in a huge variety of ways, from Pullen to Poulden, and in the 1980s was indexed in three different places on the IGI.
Poling is a village in Sussex, and probably the origin of the name. Petersfield is right on the border with Sussex, and on a main route to London, so brides might come from far and wide.

A Thomas POLLINGTON married a Mary Pescod in Rogate in 1706 (image 483 of 1022 if you click the image link on Family Search)

Rogate is only five miles from Petersfield and I can't find any Pollington children. Is it feasible that this is another surname variant?

This is a problem that has bugged me and other researchers for over thirty years, particularly irritating as the Polings were solid tradesmen - carpenters and blacksmiths - right in the centre of Petersfield, so I cannot imagine that they did not marry.