RootsChat.Com

You may have this already but the funeral notice gives details of his children, a couple of cousins and also mentions that he was of 4 Canning Road.
https://trove.nla.gov.au/newspaper/article/79941855?searchTerm=rowland%20wood
Bev

I have a rather unusual situation in my tree, in Western Australia.  My g-g-aunt married (for the first time) in 1926 at the advanced age of 52.  She lived for 13 more years, and ten years after her death her  husband married her lifetime companion and rumoured half-sister, he being 82 years old and she 84.
Needless to say, neither marriage produced offspring.
Bev

The line through 'name of father' could suggest that he was illegitimate.  The only record that fits from Lancs OPC is

Baptism: 14 Mar 1852 St Peter, Bolton, Lancashire
Thomas Wilkinson - Son of Ann Wilkinson, Spinster
    Abode: Great Bolton
    Baptised By: R. Harries Jones Curate

I'm not an expert on the geography of the region but I think Bolton would be about 10 miles from Barton.

Bev

I perhaps had a bit of luck with my 4 x great grandmother Harriet Rogers, 1797-1868 in Dorset, mother Susannah Rogers.
Her baptism records states 'base born from the workhouse'.  She was considerate enough to marry for the second time (first husband died young) as late as 1844 and named her father as John Hawkins on the marriage certificate.  I haven't found a John Hawkins who could be a likely candidate in Sherborne where she was born, but it seems to be a rather specific name to have been invented, and also mother Susannah was living with Harriet in Shepton Mallet until fairly close to the time of the wedding so I presume she would have asked her mother for this info.

More circumstantial evidence with my 5 x great grandmother Sarah Love Startup,  approx 1776-1851 in Kent.  Her mother Jane had three daughters by different men while single and later married another man.  The oldest daughter Mary Love Startup was fathered by one Robert Love, confirmed by bastardy proceedings, and it would be logical to think that he was the father of Sarah too, but I've found no evidence.  Between these two girls there was another daughter fathered by William Monktelow;  again I have the evidence for this.  There must be some documentation out there somewhere.

I agree with you that the puzzle of the father's anonymity is compelling! 
Bev