As a very crude measure of the geographical spread of Pelan and related surnames in Ireland, I have taken data from the LDS 'pilot' transcriptions of their microfilm copies of the civil registration indices. There are a number of problems doing this, not least that the data excludes that of Northern Ireland post-1922 and so is biased in that regard. There are also transcription errors, double counting and other errors in the original source data. However, recognising the short-comings of the data and the crudity of this method, let's just take a look at what it might suggest.
The counts are for all registered events, i.e. births, marriages and deaths. The total column is pan-Ireland (thirty-two counties) and Ulster is the nine county province. The percentages are rounded to the nearest integer.
There are only three entries for Pealing (2 Belfast, 1 Lisburn) and one each of Paling and Pailing (both Belfast).
Conclusions?
Pelan is an Ulster surname, highly concentrated in counties Antrim and Down.
Despite being fairly common in Ireland, Phelan is virtually unknown in Ulster - this means the surname (which is native Irish) does not arise at all or the convention may be to spell/pronounce it as something else.
Both Pelling and Pullan are concentrated in Ulster whereas Pullen and Polan are not, suggesting that Pelan may be related to Pelling or Pullan.
Pealing, Paling and Pailing look suspiciously like variations on Pelan.
The Griffiths Valuation (1848 - 1864) recorded privately held land, those who lived on it and those who owned it. As such, it also suffers from significant bias as only the main occupying family will be represented and they indeed may be over-represented geographically as one related family may hold many plots in the same area, or there may be a greater number of smaller plots etc.
The data is based on searches using AskAboutIreland - other transcribed sources may differ and there may be errors. The following tables lists those occupying the land (not the owners):
By way of comparison with the BMD data above, we can see higher representation of the Polans but we can't really infer too much from this data. Note there are no Palen/Palins. The Pallons do not register either despite appearing above. (Mc)Polan and (Mc)Polin are almost exclusive to Down.